The beta release notes are available in the Software Update window and also in the Version History section of the manual (in the Help menu).

We do not recommend using a macOS beta on your main Mac, as there may be bugs that we have not had time to, or cannot, work around. With that said, we do welcome bug reports so that we can investigate any bugs and report them to Apple or try to develop workarounds. Please submit any feedback or bug reports via e-mail, rather than posting here.

When the new version of macOS is finalized and released to everyone, we (usually within hours) test SpamSieve with the release version and finalize the new version of SpamSieve. The new version is announced on the SpamSieve mailing list, blog, and Twitter feed and becomes available via the Software Update… command. It’s best to update SpamSieve before updating macOS. To prevent macOS from updating itself without asking you, go to the App Store section of System Preferences and make sure that Install macOS updates is unchecked.

The current beta version is SpamSieve 2.9.29b3, which adds preliminary support for macOS 10.12 High Sierra Developer Beta 1.

"Click this link (after installing SpamSieve) to join the public beta program "
The link does nothing

You need to have SpamSieve installed and launched at least once before clicking the link. Then the link will open SpamSieve and adjust the preferences so that it checks for new beta versions. You will get an alert window confirming this.